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A255322
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a(n) = Product_{k=0..n} (k^2)!.
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16
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1, 1, 24, 8709120, 182219087869378560000, 2826438545846116156142906806150103040000000000, 1051416277636507481568264360276689674557030810000137484550133942059008000000000000000000
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OFFSET
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ c * n^((2*n + 1)*(2*n^2 + 2*n + 3)/6) * (2*Pi)^(n/2) / exp(5*n^3/9 + n^2/2 + n), where c = A255504 = 3.048330306522348566911920417337613015885313475... .
a(n) = Product_{j=1..n^2} j^(n - ceiling(sqrt(j)) + 1).
a(n) = (n^2)!^n * (n!)^2 / Product_{j=1..n^2} j^(floor(sqrt(j))). (End)
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MATHEMATICA
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Table[Product[(k^2)!, {k, 0, n}], {n, 0, 10}]
Table[(n^2)!^(n+1) / Product[j^(Ceiling[Sqrt[j]]), {j, 1, n^2}], {n, 0, 6}] (* Vaclav Kotesovec, Apr 23 2024 *)
Table[(n^2)!^n * (n!)^2 / Product[j^(Floor[Sqrt[j]]), {j, 1, n^2}], {n, 0, 6}] (* Vaclav Kotesovec, Apr 23 2024 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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